A079486 Number of different solutions to a variant of the 3-ball tennis ball problem.

3, 15, 103, 879, 8787, 99061, 1227369, 16409937, 233588249, 3504149013, 54963273921, 895797910129, 15094359120933, 261882874511985, 4662472442136561, 84940003965749601, 1579633610378515989, 29927014639635474589, 576597813697577550447, 11280469732919709557493

Offset: 1

Author

Barry Cipra, Jan 19 2003

Keywords

• nonn
• changed

Comments

You're given labeled balls three at time (labeled 1,2,3 then 4,5,6 etc.), choose two balls from those still on hand (including the three you've just been given) and throw the larger out the window onto the front lawn, the smaller onto the back lawn.

a(n) is the number of 2 X n matrices of positive integers, with the numbers in each row and column increasing, the numbers in column k less than or equal to 3k and no number used more than once.

Links

• Kevin Ryde, Table of n, a(n) for n = 1..325
• Sean A. Irvine, Java program (github)
• Kevin Ryde, PARI/GP Code and Notes

Crossrefs

Cf. A000108, A001764, A002293, A049235.

Programs

PARI

\\ See links.

Extensions

Larger terms through to a(12) computed by Matt Richey.

a(13) onwards from Sean A. Irvine, Aug 17 2025